@TechReport{TR152,
  author      = "Luca Boccia",
  title       = "Efficient contraction kernel selection with a knight's move",
  institution = "PRIP, TU Wien",
  number      = "PRIP-TR-152",
  year        = "2022",
  url         = "https://www.prip.tuwien.ac.at/pripfiles/trs/tr152.pdf",
  abstract    = "Irregular image pyramids built with combinatorial map representations of graphs (Combinatorial Pyramids) enable the usage of topological information for both down-sampling and up-sampling, used for compactness and for surface reconstruction respectively. The hierarchy and the complexity of the image pyramid are mainly controlled by the choice of a contraction kernel. In this work we propose a formal grammar for selecting contraction kernels for plateau regions in binary and multi-label images. Our method enables parallel computing through selection of independent edges to contract, and efficiency is achieved by finding a good balance between the number of contraction and simplification operations, needed after the application of the kernel. We show that our method achieves regularity and produces pyramids of height similar to regular pyramid schemes on plateau regions. Finally, we present possible solutions to generalize our approach to design a Connected Component Labeling algorithm that is both efficient and correct."
}